• Chapter 1 Introduction
  • 1.1 Isogeometric Analysis
  • 1.2 Fracture mechanics and eXtended Finite Element Method
  • 1.3 eXtended Isogeometric Analysis (XIGA)
• Chapter 2 Introduction to Isogeometric Analysis
  • 2.1 Isogeometric Analysis Method
    • 2.1.1 Computational Geometry
  • 2.2 Basic Terminologies
  • 2.3 B-splines
    • 2.3.1 Knot vector
    • 2.3.2 Basis Functions
    • 2.3.3 Derivatives of B-spline basis functions
    • 2.3.4 B-spline geometries
      • 2.3.4.1 B-spline curves
      • 2.3.4.2 B-spline surfaces
      • 2.3.4.3 B-spline solids
    • 2.3.5 Refinement
      • 2.3.5.1 Knot insertion
      • 2.3.5.2 Order Elevation
  • 2.4 Non-Uniform Rational B-Splines (NURBS)
  • 2.5 NURBS drawbacks
    • 2.5.1 Local refinement
    • 2.5.2 Patch Assembly
  • 2.6 T-splines
    • 2.6.1 PB-Splines
    • 2.6.2 Defining T-splines
      • 2.6.2.1 Anchors and T-mesh
      • 2.6.2.2 Building a T-spline
  • 2.7 Isoparametric concept
  • 2.8 Obtaining weak form of BVPs
  • 2.9 Similarities and differences for Isogeometric analysis and Finite element analysis
• Chapter 3 Discretization and Linear Elasticity Problems
  • 3.1 Formulating the equation
    • 3.1.1 Strong form of BVP
    • 3.1.2 Weak Form of Equilibrium equation
      • 3.1.2.1 Galerkin’s method
  • 3.2 One Dimensional Poisson’s Equation
  • 3.3 Infinite plate with circular hole under constant in-plane tension
• Chapter 4 Fracture Mechanics, A review
  • 4.1 Historical perspective
  • 4.2 Westergaard analysis of a sharp crack
  • 4.3 Stress Intensity Factor (SIFs)
  • 4.4 Griffith theory of strength
  • 4.5 Brittle Materials
  • 4.6 Mixed mode crack propagation
  • 4.7 J-integral method for calculation of SIFs
  • 4.8 Some numerical method based on J-integral method
    • 4.8.1 Equivalent domain integral method
    • Li et al [23] proposed the equivalent domain integral method as an alternative approach, which requires only one analysis. According to Fig. 2.17b, the J integral can be defined as ( [23,24]):
    • 4.8.2 Interaction integral method
• Chapter 5 Extended finite element method
  • 5.1 A review of XFEM development
  • 5.2 Basics of XFEM
    • 5.2.1 Partition of unity
    • 5.2.2 Enrichment
      • 5.2.2.1 Intrinsic enrichment
      • 5.2.2.2 Extrinsic enrichment
  • 5.3 Enrichment in extended finite element method
    • 5.3.1 The Heaviside function
    • 5.3.2 Asymptotic functions
  • 5.4 XFEM discretization
  • 5.5 Element integration
• Chapter 6 Extended isogeometric analysis for modeling crack growth problems
  • 6.1 Introduction
  • 6.2 Need for XIGA
  • 6.3 Enrichment in XIGA
  • 6.4 Numerical examples
    • 6.4.1 A rectangular plate with an edge crack
    • 6.4.2 An infinite plate with a middle crack under uniform uniaxial in-plane tension
    • 6.4.3 Propagating crack through a T-spline patch of plate with a middle crack under uniform in-plane tension
    • 6.4.4 A plate with two circular holes and two edge crack under displacement control state
• Chapter 7 Conclusion and future works
  • 7.1 Conclusion
  • 7.2 Future works

...see more